**Answer:**

a)11,71 m/s

b)12.73 m/s

**Explanation:**

We apply the conservation principle because there is no friction between the hill and the sled:

Total initial energy (Ei) = Total initial energy (Ef), Equation(1)

We define:

K = Kinetic energy =

U = Potential energy =

m = mass (kg)

v = velocity (m/s)

h = height (m)

g = gravity acceleration =

A) hi=7m, hf=0 ,vi=0 , vf=?

** **

**Answer: She reaches the base of the hill with speed of 11.22 m/s**

**B) **hi=7 m, vi=5 m/s, hf=0**, vf=?**

**We divide all terms by m**

**Answer:** She will move with a speed of 12.73 m/s when she reaches the base of the hill

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**Answer:**

**θ = (7π / 3) rad**

**Explanation:**

given,

displacement of simple harmonic motion along x-axis

equation is given as

x = 5 sin (π t + π/3 )

general equation of simple harmonic motion

x = A sin θ

θ is the phase angle

θ = π t + π/3

at t = 2 s

Phase of the motion at t =2 s is **θ = (7π / 3) rad**

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